Show that for a first order reaction, time required 99.9% of reaction to complete is 10 t

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Blazing goIITian

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k = 2.303 /t . log [ a-x ] / [ a] ----A

where k is rate of reaction

t ----time taken

a ----initial concentration

x -- reactants those converted into products

we know that

t1/2 = half life

k = 0.693/t50%------1

u can derive ---1 by putting x = a/2 in ---A

for 99% reaction to be completed we have a = 100

x =99.9

from ---A

k = 2.303/t . log [ 100] / [ 100-99.9]

k = 2.303 /t 99% . log [ 100]/[ 0.1]

k = 2.303/t99% . log [ 10^3]

k = [2.303 . 3] / t99%----2

equate 1 and 2

we have k = 0.693/ t50% = 2.303 * 3 / t99%

t99% / t50% = 2.303 * 3 / 0.693 = 9.97 = 10[ approx]

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